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A firm produces two goods. The inverse demand functions are given by P1 = 100 - 2Q1 + Q2 and P2 = 75 + 2Q1 - Q2. The total cost of production is given by TC = 1000 + 20Q1 + 10Q2 + 201Q2. a. If the firm cannot produce more than 50 units in total due to capacity constraints, how much of each good will they produce? b. Interpret the value of the Lagrange multiplier at the optimal solution from part (a)